Appendix B: Models to Project Net Income and Stressed Capital

This appendix describes the models used to project stressed capital ratios and pre-tax net income and its components for the 18 BHCs subject to DFAST 2013.27 The models fall into four broad categories:

Models to project losses on loans held in the accrual loan portfolio.

Models to project other types of losses, including those from changes in fair value on loans held for sale or measured under the fair-value option, securities, trading and counterparty exposures, losses related to operational-risk events, and mortgage repurchase/put-back losses.

Models to project the components of PPNR (revenues and non-credit-related expenses).

The model to project capital ratios, given projections of pre-tax net income, assumptions for determining provisions into the ALLL, and assumed capital actions under the Dodd-Frank Act stress test rule.

A majority of the models described here were refined incrementally over the past year--in some instances, benefitting from more granular data collection through the FR Y-14 report. However, some of the models were either changed substantially or newly implemented for DFAST 2013, including the commercial real estate mortgage model, the credit card model, the modeling of losses due to operational-risk events, and the PPNR model.

More than a dozen individual models are used to project losses on loans held in the accrual loan portfolio. The individual loan types modeled can broadly be divided into wholesale loans, such as commercial and industrial (C&I) loans and commercial real estate (CRE) loans, and retail loans, including various types of residential mortgages, credit cards, student loans, auto loans, small business loans, and other consumer lending. In some cases, these major categories comprise several subcategories, each with its own loss projection model, but the models within a subcategory are similar in structure and approach. The models project losses using detailed loan portfolio data provided by the BHCs on the FR Y-14 report.

Two general approaches are taken to model losses on the accrual loan portfolio. In the first approach--an approach broadly used for DFAST 2013--the models estimate expected losses under the macroeconomic scenario; that is, they project the probability of default (PD), loss given default (LGD), and exposure at default (EAD) for each quarter of the planning horizon. Expected losses in quarter t are the product of these three components:

Losst = PDt * LGDt * EADt

PD is generally modeled as part of a transition process in which loans move from one payment status to another (e.g., from current to delinquent) in response to economic conditions. Default is the last possible transition and PD represents the likelihood that a loan will default during a given period. The number of payment statuses and the transition paths modeled differ by loan type.

LGD is typically defined as a percentage of EAD and is based on historical data. For some loan types, LGD is modeled as a function of borrower, collateral, or loan characteristics and the macroeconomic variables from the severely adverse scenario. For other loan types, it is assumed to be a fixed percentage for all loans in a category. Finally, the approach to EAD varies by loan type and depends on whether the outstanding loan amount can change between the current period and the period in which the loan defaults (e.g., for lines of credit).

In the second approach, the models capture the historical behavior of net charge-offs relative to changes in macroeconomic and financial market variables and loan portfolio characteristics.

The loss models primarily focus on losses arising from loans in the accrual loan portfolio as of September 30, 2012. The loss projections also incorporate losses on loans originated or purchased after the planning horizon begins. These incremental loan balances are calculated based on the BHCs' own projections of loan balances over the planning horizon under the severely adverse scenario. These balances are assumed to have the same risk characteristics as those of the loan portfolio as of September 30, 2012, with the exception of loan age in the retail portfolios, where seasoning is incorporated. This is a simple, but generally conservative, assumption.

Loss projections generated by the models are adjusted to take account of purchase accounting treatment, which recognizes discounts on impaired loans acquired during mergers, and any other write-downs already taken on loans held in the accrual loan portfolio. This latter adjustment ensures that losses related to these loans are not double-counted in the projections.

Wholesale Lending: Corporate Loans

Losses stemming from default on corporate loans are projected at the loan level using an expected-loss modeling framework. Corporate loans consist of a number of different categories of loans, as defined by the FR Y-9C. The largest group of these loans include C&I loans, which are generally defined as loans with more than $1 million in committed balances and are "graded" using a BHC's corporate loan rating process.28

The PD for a C&I loan is projected over the planning horizon by first calculating the loan's PD at the beginning of the planning horizon and then projecting it forward using an estimated equation that relates historical changes in PD to changes in the macroeconomic environment. The PD as of September 30, 2012, is calculated for every C&I loan in a BHC's portfolio using detailed, loan-level information submitted by the BHC. For publicly traded borrowers, a borrower-specific PD, based on the expected default frequency, is used. For other borrowers, the PD is estimated based on the BHC's internal credit rating, which is converted to a standardized rating scale. Loans that are 90 days past due, in non-accrual status, or that have an ASC 310-10 reserve as of September 30, 2012 are assigned a PD of 100 percent.

Quarterly changes in the PD after the third quarter of 2012 are projected over the planning horizon using a series of equations that relate historical changes in the average PD as a function of changes in macroeconomic variables, including changes in real GDP, the unemployment rate, and the spread on BBB-rated corporate bonds. The equations are estimated separately by borrower industries, credit quality categories, and countries.

The LGD for a C&I loan at the beginning of the planning horizon is determined by the line of business, seniority of lien (if secured), country, and ASC 310-10 reserve, if applicable. The LGD is then projected forward by relating the change in the LGD to changes in the PD. In the model, the PD is used as a proxy for economic conditions, and, by construct, increases in PD generally lead to higher LGDs.

The EAD for closed-end C&I loans is assumed to equal the loan's outstanding balance. The EAD for C&I revolving lines of credit equals the sum of the funded balance and a portion of the unfunded commitment, which reflects the amount that is likely to be drawn down by the borrower in the event of default. This drawdown amount was estimated based on the historical drawdown experience for defaulted U.S. syndicated loans that are in the Shared National Credit (SNC) database.29 The EAD for standby letters of credit and trade finance credit are conservatively assumed to equal the total commitment.

Other corporate loans that are similar in some respects to C&I loans are modeled using the same framework. These loans include owner-occupied commercial real estate loans, capital equipment leases, loans to depositories, and other loans.30 Projected losses for these loans are disclosed in the other loans category.

Wholesale Lending: Commercial Real Estate Mortgages

CRE mortgages are loans collateralized by domestic and international multifamily or non-farm, non-residential properties, and construction and land development loans (C&LD), as defined by the FR Y-9C. Losses stemming from default on CRE mortgages are projected at the loan level using an expected-loss modeling framework.

The PD model for CRE mortgages is a hazard model of the probability that a loan transitions from current to default status, given the characteristics of the loan as well as macroeconomic variables, such as house prices and CRE vacancy rates, at both the geographic market and national level. Once defaulted, the model assumes the loan does not re-perform; the effect of re-performance on the estimated loan loss is captured in the LGD model. A CRE mortgage loan is considered in default if it is 90 days past due, in non-accrual status, has an ASC 310-10 reserve, or had a very low internal credit rating at the most recent time its maturity was extended. The effect of seasoning and loan maturity on the PD is estimated to be different for income-producing and C&LD loans, and is estimated separately for each loan type using historical FR Y-14 data. However, the effect of other loan characteristics and the macroeconomic variables is assumed to be the same for income-producing properties and C&LD loans and is estimated using a single model for both types of loans using historical CMBS data.

The LGD for CRE mortgages is estimated using Y-14 data on ASC 310-10 reserves. The model first estimates the probability that a defaulted loan will have losses as a function of loan characteristics and macroeconomic variables, and then, using loans with losses, estimates the loss on the CRE mortgage, as a function of the expected probability of loss, characteristics of the loan, and macroeconomic variables. Finally, the EAD for CRE mortgages is assumed to equal the loan's outstanding balance for amortizing loans and the full committed balance for C&LD loans.

Retail Lending: Residential Mortgages

Residential mortgages held in BHC portfolios include first and junior liens, either closed-end loans or revolving credits, that are secured by one- to-four-family residential real estate as defined by the FR Y-9C. Losses stemming from default on residential mortgages are projected at the loan level using an expected-loss modeling framework.31

The PD model for first-lien residential mortgages estimates the probability that a loan transitions to different payment statuses, including current, delinquent, default, and paid off. Separate PD models are estimated for three types of closed-end, first-lien mortgages: fixed-rate, adjustable-rate, and option adjustable-rate mortgages. The PD model specification varies somewhat by loan type, but in general, each model estimates the probability that a loan transitions from one payment state to another (e.g., from current to delinquent or from delinquent to default) over a single quarter, given the characteristics of the loan, borrower, and underlying property as well as macroeconomic variables such as local house prices, the statewide unemployment rate, and interest rates.32 Origination vintage effects are also included in part to capture unobserved characteristics of loan quality. The historical data used to estimate this model are industry-wide, loan-level data from many banks and mortgage loan originators. These estimated PD models are used to simulate default associated with the severely adverse scenario for each loan reported by each BHC. Loans that are 180 days or more past due as of September 30, 2012, are considered in default and are assigned a PD of 100 percent.

The LGD for residential mortgages is estimated using two models. One model estimates the amount of time that elapses between default and real estate owned (REO) disposition (timeline model), while the other relates characteristics of the defaulted loan, such as the property value at default, to one component of losses net of recoveries--the proceeds from the sale of the property net of foreclosure expenses (loss model).33 These net proceeds are calculated from historical data on loan balances, servicer advances, and losses from defaulted loans in private-label mortgage-backed securities (RMBS). These RMBS data are also used to estimate the LGD loss model separately for prime jumbo loans, subprime, and alt-A loans.34

Finally, using the elapsed time between default and REO disposition estimated in the timeline model, total estimated losses are allocated into credit losses on the defaulted loans, which are fully written down at the time of default, or net losses arising from the eventual sale of the underlying property (other real estate owned--or OREO--expenses), which flow through PPNR. House price changes from the time of default to foreclosure completion (REO acquisition) are captured in LGD, while house price changes after foreclosure completion and before sale of the property are captured in OREO expenses. The LGD for loans already in default as of September 30, 2012, includes further home price declines through the point of foreclosure.

Home equity loans (HELs) are junior-lien, closed-end loans, and home equity lines of credit (HELOCs) are revolving open-end loans extended under lines of credit, both secured by one- to four-family residential real estate as defined by the FR Y-9C. Losses stemming from default on HELs and HELOCs are projected at the loan level in an expected loss framework that is similar to first-lien mortgages, with a few differences. In the PD model for HELs and HELOCs, the delinquency state is defined as ever delinquent, to simplify the competing risk-model structure. The model also assumes that second-lien HELs and HELOCs that are current as of September 30, 2012, but are behind a seriously delinquent first-lien will all default within the planning horizon. The LGD for HEL and HELOCs is estimated using data from private-label mortgage-backed securities, using the same models used for closed-end first-lien, but the estimated total mortgage losses for properties with a defaulted HEL or HELOC are allocated based on the lien position. Finally, for HELOCs, EAD is conservatively assumed to equal the credit limit.

Retail Lending: Credit Cards

Credit cards include both general purpose and private-label credit cards, as well as charge cards, as defined by the FR Y-9C. Credit card loans extended to individuals are included in retail credit cards, while credit cards loans extended to businesses and corporations are included in other retail lending and are modeled separately. Losses stemming from defaults on credit cards are projected at the loan level using an expected-loss modeling framework.

The PD model for credit cards estimates the probability that a loan transitions from delinquency status to default status, given the characteristics of the account and borrower as well as macroeconomic variables such as unemployment. When an account defaults, it is assumed to be closed and does not return to current status. Credit card loans are considered in default when they are 120 days past due. Because the relationship between the PD and its determinants can vary with the initial status of the account, separate transition models are estimated for accounts that are current and active, current and inactive accounts, and delinquent accounts. In addition, because this relationship can also vary with time horizons, separate transition models are estimated for short-, medium-, and long-term horizons. The historical data used to estimate this model are industry-wide, loan-level data from many banks, and separate models were estimated for bank cards and charge cards. The PD model is used to forecast the PD for each loan reported by each BHC in the Y-14M report.

The LGD for credit cards is assumed to be a fixed percentage and is calculated separately for bank cards and charge cards based on historical industry data on LGD during the most recent economic downturn. The EAD for credit cards equals the sum of the amount outstanding on the account and a portion of the credit line, which reflects the amount that is likely to be drawn down by the borrower between the beginning of the planning horizon and the time of default. This drawdown amount is estimated as a function of account and borrower characteristics. Because this relationship can vary with the initial status of the account and time to default, separate models are estimated for current and delinquent accounts and for accounts with short-, medium-, and long-term transition to default. For accounts that are current, separate models were also estimated for different credit-line-size segments.

Retail Lending: Auto

Auto loans are consumer loans extended for the purpose of purchasing new and used automobiles and light motor vehicles as defined by the FR Y-9C. Losses stemming from default in auto retail loan portfolios are projected at the portfolio segment level using an expected loss framework.

The PD model for auto loans estimates the probability that a loan transitions from either a current or delinquent status to default status, given the characteristics of the loan and borrower as well as macroeconomic variables such as house prices and the unemployment rate (which, in some cases, are interacted with loan and borrower characteristics to allow for greater sensitivity to stressful conditions in high-risk segments). Default on auto loans is defined based on either the payment status (120 days past due), actions of the borrower (bankruptcy), or the lender (repossession). Because the relationship between the PD and its determinants can vary with the initial status of the account, separate transition models are estimated for accounts that are current and delinquent accounts. The historical data used to estimate this model are loan-level, credit bureau data.

The LGD for auto loans is estimated given the characteristics of the loan as well as macroeconomic variables. The historical data used to estimate this model are pooled, segment-level data provided by the BHCs on the FR Y-14Q. The EAD for auto loans is based on the typical pattern of amortization of loans that ultimately defaulted in historical credit bureau data. The estimated EAD model captures the average amortization by loan age for current and delinquent loans over nine quarters.

Retail Lending: Other Retail Lending

Other retail lending includes the small business loan portfolio, the other consumer loan portfolio, the student loan portfolio, the business and corporate credit card portfolio, and international retail portfolio. Losses due to default on other retail lending are forecast by modeling net charge-off rates as a function of portfolio risk characteristics and macroeconomic variables, then using this model to predict future charge-offs consistent with the macroeconomic variables provided in the severely adverse scenario.35 The predicted net charge-off rate is applied to balance projections provided by the BHCs to estimate projected losses. Default is defined as 90 days or more past due for domestic and international other consumer loans and 120 days or more past due for student loans, small business loans, corporate cards, and international retail portfolios. The net charge-off rate is modeled in a system of equations that also includes the delinquency rate and the default rate. In general, each rate is modeled in an autoregressive specification that also includes the rate in the previous delinquency state, characteristics of the underlying loans, macroeconomic variables and, in some cases, seasonal factors. The models are specified to implicitly capture roll-rate dynamics. In some cases, the characteristics of the underlying loans, such as dummy variables for each segment of credit score at origination, are also interacted with the macroeconomic variables to capture differences in sensitivities across risk segments to changes in the macroeconomic environment. Each retail product type is modeled separately and, for each product type, economic theory and the institutional characteristics of the product guide the inclusion and lag structure of the macroeconomic variables in the model.

Because of data limitations and the relatively small size of these portfolios, the net charge-off rate for each loan type is modeled using industry-wide, monthly data at the segment level. For most portfolios, these data are collected on the FR Y-14Q Retail schedule, which segments each portfolio by characteristics such as borrower credit score; loan vintage; type of facility (e.g., installment versus revolving); and, for international portfolios, geographic region.36

Charge-off rates are projected by applying the estimated system of equations to each segment of the BHC's loan portfolio as of September 30, 2012. The portfolio level charge-off rate equals the dollar-weighted average of the segment-level charge-off rates.37 These projected charge-off rates are applied to the balance projections supplied by the BHC to calculate portfolio losses.

Loan-Loss Provisions for the Accrual Loan Portfolio

Losses on the accrual loan portfolio flow into net income through provisions for loan and lease losses. Provisions for loan and lease losses equal projected loan losses for the quarter plus the amount needed for the ALLL to be at an appropriate level at the end of the quarter, which is a function of projected future loan losses. The appropriate level of ALLL at the end of a given quarter is generally assumed to be the amount needed to cover projected loan losses over the next four quarters.38 Because this calculation of ALLL is based on projected losses under the severely adverse scenario, it may differ from a BHC's actual level of ALLL at the beginning of the planning horizon, which is based on the BHC's assessment of future losses in the current economic environment. Any difference between these two measures of ALLL is smoothed into the provisions projection over the nine quarters of the planning horizon. Because projected loan losses include off-balance sheet commitments, the BHC's allowance at the beginning of the planning horizon for credit losses on off-balance sheet exposures (as reported on the FR Y-9C) is subtracted from the provisions projection in equal amounts each quarter.

Loans Held for Sale or Measured under the Fair-Value Option

Certain loans are not accounted for on an accrual basis. Loans to which the fair-value option (FVO) is applied are valued as mark-to-market assets; loans under the held-for-sale (HFS) and some loans under the held-for-investment (HFI) accounting classifications are carried at the lower of cost or market value. FVO, HFS, and HFI loan portfolios are identified by the BHCs and reported on the FR Y-14. Losses related to FVO, HFS, and HFI loans are recognized in the income statement at the time of the devaluation.

For the six BHCs subject to the global market shock, changes in the value of these loans are calculated using the price shocks applied to similar loans in other mark-to-market positions on the BHCs' balance sheets (e.g., trading account positions). For the remaining BHCs, losses on FVO, HFS, and HFI loans are not projected separately, and any gains or losses on these loans are captured in PPNR as part of non-interest income. The PPNR model is described later in this paper (see page 46).

For the six BHCs subject to the global market shock, losses on C&I loans held under FVO, HFS, and HFI accounting standards are estimated by applying the percent change in the secondary market prices for corporate loans during the second half of 2008 to current outstanding and committed loan balances. The loss rates applied to C&I loans vary with the credit rating reported by the BHCs and with the amount funded. Loss rates for investment-grade loans with more than half of their credit line used are based on historical price changes for investment grade loans, while loss rates for investment-grade loans with less than half of their credit line used are based on changes in CDS spreads. Loss rates for all non-investment grade loan facilities, regardless of the percent funded, are based on price changes for loans with the same credit rating.

Losses on CRE and retail loans held under FVO, HFS, and HFI accounting standards are estimated in a similar way. The loss rate applied to these loans are taken from the global market shock and vary by major type of loan (e.g., residential mortgages, student loans, credit cards, and the major categories of CRE loans) and by loan vintage (year of origination). Losses on all major residential and other retail asset types (including student loans and credit cards) are estimated applying a percent change in value based on the loan type and vintage to the carrying value of FVO and HFS exposures provided by the firms. Because retail FVO and HFS loans are generally of relatively high credit quality, the changes in value are based on the global market shock for AAA-rated positions in the non-agency residential whole loans, credit card asset-backed securities (ABS), auto ABS, and student loan ABS portfolios. No losses are assumed for residential mortgage loans under forward contract with the government-sponsored enterprises (GSEs).

Securities in the Available-for-Sale and Held-to-Maturity Portfolios

Losses on securities held in the available-for-sale (AFS) or held-to-maturity (HTM) portfolios are projected other-than-temporary impairment (OTTI) over the planning horizon. OTTI projections incorporate other-than-temporary differences between amortized cost and fair market value due to credit impairment, but not differences reflecting changes in liquidity or market conditions.

Some of the AFS/HTM securities, including U.S. Treasury and U.S. government agency obligations and U.S. government agency mortgage-backed securities (MBS), are assumed not to be at risk for the kind of credit impairment that results in OTTI charges. The remaining securities can be grouped into two basic categories: securitizations, where the value of the security depends on the value of an underlying pool of collateral, and direct obligations such as corporate or sovereign bonds, where the value of the security depends primarily on the credit quality of the issuer.39

In all, 10 separate models are used to project OTTI, reflecting differences in the basic structure of the securities (securitized versus direct obligation) and differences in underlying collateral and obligor type. Overall, the OTTI projections involve CUSIP-level analysis of more than 70,000 individual positions at the 18 BHCs.

For securitized obligations, credit and prepayment models estimate delinquency, default, severity, and prepayment vectors on the underlying pool of collateral under the supervisory scenarios. In most cases, these projections incorporate relatively detailed information on the underlying collateral characteristics for each individual security, derived from commercial databases that contain loan-level collateral and security structure information. Delinquency, default, severity, and prepayment vectors are projected either using econometric models developed by the Federal Reserve or third-party models designed to project these estimates in stressed economic environments. The models used vary with the type of underlying collateral, but generally estimate the relationship between the collateral's performance vectors and economic variables, such as the unemployment rate and house prices. These vectors are then applied to a cash flow engine that captures the specific structure of each security (e.g., tranche, subordination, and payment rules) to calculate the intrinsic value (present value of the cash flows) for that security. If the projected intrinsic value is less than the value at which the security is being carried on the BHC's balance sheet (amortized cost), then the security is considered to be other than temporarily impaired, and OTTI is calculated as the difference between amortized cost and intrinsic value.

For direct obligations, the basic approach is to assess the PD or severe credit deterioration for each security issuer or group of security issuers over the planning horizon. PD is either modeled directly or inferred by modeling changes in expected default frequencies or credit default swap (CDS) spreads for the bonds in question. A security is considered other than temporarily impaired if the projected value of the PD or CDS spread crossed a predetermined threshold level--generally the level consistent with a CCC/Caa rating--at any point during the planning horizon. LGD on these securities is based on historical data on bond recovery rates. OTTI is calculated as the difference between the bond's amortized cost and its projected value under the supervisory scenarios.

No OTTI charges are assigned to securities acquired by the BHCs after September 30, 2012, ("incremental balances") because these are assumed to be purchased at already discounted prices. This assumption is also consistent with historical data showing that the composition of the AFS and HTM portfolios tends to shift toward U.S. Treasury and agency obligations in times of economic stress, suggesting that incremental AFS/HTM balances are less likely to be at risk of generating OTTI charges.

Trading and Counterparty Credit Risk

Total potential mark-to-market losses stemming from trading positions under a stressed market environment can be broken into two primary types. The first type of loss arises from a decrease in the market value of trading positions, regardless of the BHC's counterparties. The second type is the counterparty credit risk associated with changes in counterparty exposures and with deterioration of counterparties' creditworthiness under stressed market conditions, which adversely affects the riskiness of positively valued trading positions. The models used to project losses on trading positions under the global market shock account for both sources of potential losses, incorporate the accounting treatment of these positions, and generally rely on information provided by firms on estimated sensitivities of their exposures to specific risk factor shocks. Because positions in the trading account are mark-to-market on a daily basis, the approach used to generate loss projections on trading positions is intended to capture the market-value effect of the global market shock.

Losses on trading positions, such as equities, FX, interest rates, commodities, credit products, private equity, and other fair-value assets, arising from the global market shock are calculated using the BHCs' own estimates of the sensitivity of the value of these positions to changes in a wide range of market rates, prices, spreads, and volatilities. Trading losses are calculated by multiplying these sensitivities by the risk factor changes included in the global market shock developed by the Federal Reserve. These shocks are assumed to be instantaneous and no additional hedging, recovery in value, or changes in positions are incorporated into the loss calculation.

Counterparty credit losses capture the effect of the global market shock on counterparty exposures and on credit valuation adjustments (CVA) and incremental default risk (IDR) of the six BHCs with large trading positions. CVAs are adjustments above and beyond the mark-to-market valuation of the BHCs' trading portfolios that capture changes in the risk that a counterparty to derivatives transaction or other trading position will default on its obligations. Using detailed data provided by the six trading BHCs on the FR Y-14A Counterparty schedule, each trading firm's baseline and stressed CVA for each counterparty or ratings band is calculated as a function of unstressed and stressed values of exposure, PD, and LGD. CVA losses equal the difference between the baseline and the stressed CVAs.

In addition to CVA and mark-to-market losses on trading positions, default risk in the trading book is captured through incremental default risk (IDR). IDR estimates the potential additional loss stemming from the default of individual counterparties in excess of the CVA-related losses associated with the defaulting counterparties or obligors. IDR complements CVA in the stress tests by estimating the losses from jump-to-default in the tail of the distribution of defaults, where the tail percentile is calibrated using the corporate bond spread in the severely adverse scenario.

The IDR models estimate losses from jump-to-default for various exposure types, including single-name, index and index-tranche, securitizations, and counterparty credit, at different levels of granularity depending on exposure type. The loss estimates are based on simulation models of obligor-level defaults. The IDR loss models rely on position and exposure data provided by the firms. IDR losses occur over nine-quarters. For IDR on collateralized counterparty credit positions, the projections assume a margin period of risk after the initial market shock during which no collateral is received in response to margin calls, and default risk is elevated to reflect the funding stress from collateral calls.

Losses on trading and counterparty positions as a result of a global market shock were estimated only for the six BHCs with large trading operations since trading operations determine risk and performance to a larger extent at these firms than at any other BHCs participating in DFAST 2013. In addition, the Federal Reserve's projections of PPNR for all 18 BHCs incorporate the effect of the supervisory scenarios on the revenues generated by day-to-day trading activities, such as market-making for customers and clients.

Losses Related to Operational-Risk Events

Losses related to operational-risk events are a component of PPNR and include losses stemming from events such as fraud, employee lawsuits, or computer system or other operating disruptions. Operational-risk loss estimates are an average of losses estimated using three approaches: a panel regression model, a loss distribution approach (LDA), and a historical simulation approach. In all three models, projections of operational-risk-related losses for the 18 BHCs are modeled for each of seven operational-risk categories identified in the Federal Reserve's advanced approaches rule.40 All three models are based on historical operational-loss data submitted by the BHCs on the FR Y-14Q.

In the panel regression model, projections of losses related to operational-risk events are the product of two primary components: loss frequency and loss severity. The expected loss frequency is the estimated number of operational-loss events in the severely adverse scenario, while loss severity is the estimated loss per event in each category. Loss frequency is modeled as a function of macroeconomic variables and BHC-specific characteristics. The model is estimated using FR Y-14Q data on operational-loss events as reported by BHCs. Macroeconomic variables, such as the real GDP growth rate, stock market return and volatility, credit spread, and the unemployment rate, are included directly in the panel regression model and/or used to project certain firm-specific characteristics. Loss is projected as a product of projected loss frequency from the panel regression model and loss severity, which equals the historical dollar loss per event in each operational-risk category. Total losses related to operational-risk events equal losses summed across operational-risk categories. Because the relationship between the frequency of operational-risk events and macroeconomic conditions varies across the categories, separate models were estimated for each category.41

In the LDA model, expected losses related to operational-risk conditional on the macroeconomic scenarios are proxied by the losses at different percentiles of simulated, annualized loss distributions. The loss frequency is assumed to follow a Poisson distribution, in which the estimated intensity parameter of the Poisson distribution is specific to each event type and BHC. A loss severity distribution is also fit to each event type for each BHC.42 The distribution of aggregate annual losses is simulated, and the macroeconomic scenario is implicitly incorporated in the results through the percentile choice, which was based on analysis of historical loss data for all BHCs taken together. The approach used to choose the percentile for each scenario essentially targets the total loss forecast for all BHCs and allows the LDA approach to split this loss among the individual BHCs and event types. Loss forecasts for an individual BHC are the sum of the BHCs' loss estimates for each event type.

In the third approach--the historical simulation approach--the distribution of aggregate annual losses are simulated by repeatedly drawing the annual event frequency from the same distribution used in the LDA, but the severity of those events was drawn from historical realized loss data rather than an estimated loss severity distribution. Losses from the same percentile of the distribution as in the LDA are used to approximate the severely adverse scenario.

Mortgage Repurchase Losses

Mortgage repurchase expenses are a component of PPNR and are related to litigation, or to demands by mortgage investors to repurchase loans deemed to have breached representations and warranties, or to loans insured by the U.S. government for which coverage could be denied if loan defects are identified. Mortgage repurchase losses for loans sold with representations and warranties liability are estimated in two parts. The first part is to estimate credit losses for all loans sold by a BHC that have outstanding representations and warranties liability, including loans sold as whole loans, into private-label securities (PLS) or to a GSE (Fannie Mae and Freddie Mac) or loans insured by the government. This part takes into account both losses recognized to date and future losses projected over the remaining lifetime of the loans. The second part is to estimate the share of this credit loss that may be ultimately put back to the selling BHC (whether through contractual repurchase, a settlement agreement, or litigation loss).

Future credit loss rates for mortgages (e.g., grouped by vintage and investor type) are projected using industry-wide data and models that incorporate the house price assumptions in the severely adverse scenario.43 These industry-wide credit loss rates for the GSEs are first adjusted to reflect the relative credit performance of loans sold by each BHC and then are applied to the outstanding balances of the corresponding groups of loans reported by each BHC. These estimates are based on data provided by the BHCs, which are collected on the FR Y-14A and include vintage-level data on original and current unpaid balances, current delinquency status, and losses recognized to date, among other measures. Losses recognized to date on mortgages sold into private-label securities (PLS) and as whole loans are estimated by applying historical credit loss rates by vintage to the unpaid principal balance of the run-off portfolio.

The share of past and future credit losses likely to be ultimately put back to the selling BHCs (the "put-back rate") is estimated separately for each investor type and considers both investor behavior to date and the procedural mechanics of pursuing repurchase claims. For whole loans and loans sold into PLS, the estimated put-back rate is based on information from recent settlement activities in the banking industry and incorporates adjustments for supervisory assessments of BHC-specific put-back risk. For government-insured loans, the estimated put-back rate is also based on information from recent settlement activities. Finally, for loans sold to Fannie Mae and Freddie Mac, the estimated put-back rate is based on historical information on the repurchases of loans sold to Fannie Mae or Freddie Mac, with consideration given to the relative seasoning of each vintage and the time interval between default and demand.

The initial estimate of mortgage repurchase losses equals the estimated put-back rate applied to the corresponding credit losses for all loans sold by a BHC that have outstanding representations and warranties liability. This initial estimate is adjusted to account for various other factors.

First, because this methodology does not distinguish between originated loans and purchased loans, repurchase losses stemming from PLS are adjusted to avoid double-counting of put-back exposure related to whole loans sold to another CCAR BHC and are subsequently included in a PLS deal. Second, prior to incorporating estimated mortgage repurchase losses into a BHC's PPNR, estimated losses are reduced by the BHC's reported starting period amount of reserves for put-back losses.44 Finally, the projection assumes that a majority--but not all--of the mortgage repurchase losses projected using these techniques are realized over the planning horizon, with the losses divided equally across quarters and incorporated into the PPNR projections. This assumption attempts to balance the recognition that the resolution of repurchase issues could be a lengthy process against the desire to ensure that the severely adverse scenario projections incorporate a conservative assessment of the losses to which the BHCs could be exposed over the planning horizon.

Pre-Provision Net Revenue

PPNR is forecast using a series of autoregressive models that relate the components of a BHC's revenues and non-credit-related expenses, expressed as a share of relevant asset or liability balances, to BHC characteristics, and to macroeconomic variables.

These models are estimated using historical, merger-adjusted, panel data from the FR Y-9C. Separate models are estimated for 17 different components of PPNR, including five components of interest income, three components of interest expense, five components of noninterest non-trading income, three components of non-interest expenses, and trading revenue. When choosing the level of detail at which to model the components of PPNR, consideration is given both to the BHCs' business models and the ability to accurately model small components of revenue. Movements in PPNR stemming from operational-risk events, mortgage repurchases, or OREO, are modeled in separate frameworks, described earlier in this document. The PPNR model estimates and projections are adjusted where appropriate to avoid double-counting movements associated with these items.

The model specification varies somewhat by PPNR component. But in general, each component is related to characteristics of the BHCs, including, in some cases, total assets, asset composition, funding sources, and liabilities. In some PPNR components, these measures of BHC portfolio and business activity do not adequately capture the significant variation across BHCs, so BHC-specific controls are included in the models for these components. Macroeconomic variables used to project PPNR include yields on Treasury securities, corporate bond yields, mortgage rates, real GDP, and stock market price movements and volatility. The specific macroeconomic variables differ across equations based on statistical predictive power and economic interpretation.

Because forecasts of PPNR from trading activities are intended to include the effect of the relevant macroeconomic variables and to exclude the effect of the global market shock, net trading revenue is modeled using a median regression approach to effectively lessen the influence of extreme movements in trading revenue associated with the recent financial crisis.

Equity Capital and Regulatory Capital

The final modeling step translates the projections of revenues, expenses, losses, and provisions from the models described above into estimates of equity and regulatory capital for each BHC under the severely adverse scenario. The projected components of pre-tax net income are summed, and a consistent tax rate across all BHCs is applied to calculate after-tax net income over the projection period. Projected after-tax net income, combined with the capital action assumptions prescribed in the Dodd-Frank Act stress test rules, are used to project quarter-by-quarter changes in equity capital.45

The change in equity capital equals projected after-tax net income minus capital distributions (dividends and any other actions that disperse equity), plus any employee compensation-related issuance or other corporate actions that increase equity, plus other comprehensive income and other equity adjustments that are consistent with the Dodd-Frank Act stress test rules.

Projected changes in equity capital in turn determine changes in regulatory capital measures. These regulatory capital measures are consistent with current U.S. regulatory capital rules that limit or eliminate the recognition of certain intangible assets and unrealized gains and losses in tier 1 capital. For example, consistent with regulatory capital rules, only a limited amount of deferred tax assets is allowable in projected regulatory capital. Regulatory capital measures do not include unrealized gains and losses, but incorporate the cumulative effect of some other comprehensive income items, as projected by the BHCs, and apply the limits specified in the current U.S. regulatory capital rules.46

Regulatory capital projections were not adjusted to account for any differences between projected and actual performance of the BHCs during the time the supervisory stress test results were being produced in the fourth quarter of 2012 and the first quarter of 2013.

Capital ratios are calculated using average total assets and risk-weighted assets based on projections made by the BHCs under the severely adverse scenario. BHCs were required to project market risk-weighted assets over the planning horizon based on the market-risk capital rules that came into effect on January 1, 2013, for purposes of identifying positions subject to the market-risk rule and projecting the RWA amount of these positions.47 The BHC-provided projections were adjusted to account for differences between BHC and Federal Reserve projections of certain balance sheet items, such as the ALLL, servicing assets, and deferred tax assets.

28. All definitions of loan categories and default in this appendix are definitions used for the purposes of the supervisory stress test models and do not necessarily align with general industry definitions or classifications. Return to text

30. The corporate loan category also includes loans that are dissimilar from typical corporate loans, such as securities lending and farmland loans, which are generally a small share of BHC portfolios. For these loans, a conservative and uniform loss rate based on analysis of historical data was assigned. Return to text

31. To predict losses on new originations over the planning horizon, newly originated loans are assumed to have the same risk characteristics as the existing portfolio, with the exception of the loan age, LTV, and delinquency status. Return to text

32. The effects of loan modification and evolving modification practices are captured in the probability that a delinquent loan transitions back to current status (re-performing loans). Return to text

33. Other components of losses net of recoveries are calculated directly from available data. Private mortgage insurance is not incorporated into the LGD models. Industry data suggest that insurance coverage on portfolio loans is infrequent and cancellation or nullification of guarantees was a common occurrence during the recent downturn. Return to text

34. The differences between characteristics of mortgages in RMBS and mortgages in bank portfolios, such as loan-to-value ratio (LTV), are controlled for by including various risk characteristics in the LGD model, such as original LTV ratio, credit score, and credit quality segment (prime, alt-A, and subprime). Return to text

35. An exception is made for the government-guaranteed portion of BHCs' student loan portfolios, to which an assumed monthly PD of 1.5 percent and LGD of 3 percent is applied. Return to text

36. Business and corporate credit card portfolio data, which previously were collected on the FR Y-14Q Retail schedule, are now collected at the loan-level on the FR Y-14M Credit Card schedule and subsequently aggregated to the segment level. Return to text

37. The dollar weights used are based on the distribution reported during the last observation period. This method assumes that the distribution of loans across risk segments, other than delinquency status segments, remains constant over the projection period. Return to text

38. For loan types modeled in a charge-off framework, the appropriate level of ALLL was adjusted to reflect the difference in timing between the recognition of expected losses and that of charge-offs. Return to text

39. Equities are also held in the AFS portfolios, although in small amounts. Losses on these positions are calculated by applying market value shocks based on the equity price changes in the supervisory scenarios. Return to text

41. Operational-risk losses due to damage to physical assets, and business disruption and system failure are not expected to be dependent on the macroeconomic environment, and therefore were set equal to each BHC's average annual operational-risk loss in that category. External fraud was modeled using each BHC's average quarterly losses during the period from the beginning of the financial crisis in the third quarter of 2007 through the end of the recession in the fourth quarter of 2009. Return to text

42. Multiple candidate specifications for the distribution were fit to the data, and the final specification was chosen based on a number of criteria, including a measure of goodness-of-fit. Return to text

43. The data used to model credit losses for government-insured loans and loans sold to GSEs were loans randomly selected from an industry database. The data used to model credit losses for loans sold into private-label securities and as whole loans were loans in proxy deals chosen based on the dealer, issuer, and originator information contained in the database. Return to text

44. These netted expenses include repurchase reserves as of the third quarter of 2012 and litigation reserves as of the third quarter of 2012 that the BHC identified as being held specifically for put-back issues. Return to text

45. The Federal Reserve used the following capital action assumptions in projecting post-stress capital levels and ratios: (1) for the fourth quarter of 2012, each company's actual capital actions as of the end of that quarter; (2) for each quarter from the first quarter of 2013 through the end of 2014, each company's projections of capital included: (i) common stock dividends equal to the quarterly average dollar amount of common stock dividends that the company paid in the previous year (that is, from first through the fourth quarter of 2012); (ii) payments on any other instrument that is eligible for inclusion in the numerator of a regulatory capital ratio equal to the stated dividend, interest, or principal due on such instrument during the quarter; and (iii) an assumption of no redemption, repurchase, or issuance of any capital instrument that is eligible for inclusion in the numerator of a regulatory capital ratio, except for common stock issuances associated with expensed employee compensation. These assumptions are consistent with the capital action assumptions companies are required to use in their Dodd-Frank Act company-run stress tests. See 12 CFR 252.146(b)(2). Return to text